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C11×C13×C3⋊D21 #31825080

order18018
isoclinismisoclinic class of C3⋊D21
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC11×C13×C3⋊D21
unambiguous semidirect productC3⋊(C11×C13×D21)
unambiguous semidirect productC7⋊(C11×C13×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derived, HallC32×C7 ⋊ C2×C11×C13
HallC32×C11×C13 ⋊ D7
HallC7×C11×C13 ⋊ C3⋊D3
HallC32×C7×C13 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C13
HallC32×C13 ⋊ C11×D7
HallC32×C11 ⋊ C13×D7
HallC7×C13 ⋊ C11×C3⋊D3
HallC7×C11 ⋊ C13×C3⋊D3
SylowC32 ⋊ C11×C13×D7
SylowC7 ⋊ C11×C13×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC11×C13C3⋊D21
commutator, cosocle, hypocenterC32×C7C2×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C32×C7
UCSC1 ◁ C11×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4719 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C11×C13×D21, C11×D39⋊D21, C13×D33⋊D21, …
maximal normal subgroup ofD3×C11×C13×D21, C11×D39⋊D21, C13×D33⋊D21, …
maximal quotient ofC11×C13×C3⋊Dic21, C2×C11×C13×C3⋊D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 125);